论文信息 - The Largest Tree in a Random Graph

The Largest Tree in a Random Graph

Abstract In this paper we study the problem of finding the largest tree in a random graph. First of all, we estimate the size of the largest tree almost surely. Then we propose two approximate greedy algorithms. Both algorithms achieve a solution whose value is one half of the value of the optimal solution, with high probability.

Marco Protasi | Alberto Marchetti-Spaccamela

[1] L. Pósa,et al. Hamiltonian circuits in random graphs , 1976, Discret. Math..

[2] Kai Lai Chung,et al. A Course in Probability Theory , 1949 .

[3] Leslie G. Valiant,et al. Fast probabilistic algorithms for hamiltonian circuits and matchings , 1977, STOC '77.

[4] G. Grimmett,et al. On colouring random graphs , 1975 .

[5] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6] Mihalis Yannakakis,et al. The Effect of a Connectivity Requirement on the Complexity of Maximum Subgraph Problems , 1979, JACM.

[7] Giorgio Ausiello,et al. Probabilistic Analysis of the Performance of Greedy Strategies over Different Classes of Combinatorial Problems , 1981, FCT.

[8] B. Bollobás,et al. Cliques in random graphs , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.